Finding a rate of sphere area increase given its volume increaseVolume of sphere, V = 4 3 π r 3 Surface area of sphere S = 4 π r 2 .If we know, d V d t = R.Let us consider both volume and area as composite functions, thus d V d t = d V d r × d r d t = 4 π r 2 × d r d t = Rwhence d r d t = R 4 π r 2 since d S d t = 6 π r d r d t , let the value of the d r d t into the second equation, to get the answer. Is this approach logically correct?

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Finding a rate of sphere area increase given its volume increaseVolume of sphere,   V  =            4      3        π      r    3  Surface area of sphere   S  =  4  π      r    2  .If we know,                     d        V                    d        t              =  R.Let us consider both volume and area as composite functions, thus                     d        V                    d        t              =                    d        V                    d        r              ×                    d        r                    d        t              =  4  π      r    2    ×                    d        r                    d        t              =  Rwhence                     d        r                    d        t              =            R              4        π                  r          2                     since                     d        S                    d        t              =  6  π  r                    d        r                    d        t            , let the value of the                     d        r                    d        t             into the second equation, to get the answer. Is this approach logically correct?

Steppkelk · Accepted Answer

Step 1Everything is fine until you didwhence                     d        r                    d        t              =            R              4        π                  r          2                     since                     d        S                    d        t              =  6  π  r                    d        r                    d        t            .            d      S              d      t        =  8  π  r            d      r              d      t      Step 2Therefore             d      S              d      t        =  8  π  r      R          4      π              r        2            and finally             d      S              d      t        =            2      R        r

Finding a rate of sphere area increase given its volume increase. Volume of sphere, V=4/3 pi r^3. Surface area of sphere S=4pi r^2. If we know, (dV)/dt=R

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